In the context of optimization, it immediately follows from our main theorem that local maximization (in the GD-FixedPoint sense) of an arbitrary smooth function can be reduced to an optimization of a degree 5 polynomial.
Very recentlyIn fact, [1]} was developed concurrently and independently to a previous version of our paper. The proofs in this version (while still unfortunately long) have been simplified significantly since [1]} show that GD-FixedPoint is already hard in only two dimensions. [1]} proved that GD-FixedPoint is \(\cap \) -complete. We therefore obtain the following corollaries:
